The primary intention of this thesis is the study of waves and instabilities in dense plasma objects. This study seeks its applications and importance in large and small scale plasmas like the astro-physical plasma and, the nano-structures in metallic and semiconductor plasmas etc. By now the dense plasmas have the involvement of modified pressure laws, some new forces raised from the quantum potentials known as the quantum forces and the Bohr magnetization containing half spin information which affect the waves and instabilities. Three papers are included in this thesis. Low frequency electrostatic lower hybrid waves and their instabilities are examined in chapter 3. These low frequency waves are excited taking an external electron beam as a source of energy in a semiconductor magnetized plasmas. The theoretical model known as quantum hydrodynamic is used for the mathematical study which consists upon different quantum features like Fermi statistical pressure, tunneling phenomenon and the exchange and their correlated effects. On varying different normalized parameters including uniform speed of the electron beam, angle of propagation between the z-axis and the wavevector, gyro- frequency and thermal temperature of the electron beam the subsequent effects are studied. It is observed that the instability is increased by increasing the streaming speed and the ratio of electron and holes number densities and the magnetic field at some angle with the propagation direction. Later, working on the same footings in semiconductor plasmas the study of electrostatic hole-cyclotron waves is presented in chapter 4. In this case, phase speed of said waves under consideration is taken minor in the comparison of speed of streaming electrons, that is, “k .v0>>ω” where electrons of the medium are considered inertia-less. Finally, the extended study of the chapter no 4, is presented chapter 5 that deals with high frequency regime of the electrostatic electron cyclotron waves. Moreover the electron acoustic waves as a special case. In addition to the conditions discussed the propagating wave frequency is taken to be smaller in comparison to the electron gyro-frequency “ω<<ωce”. It is observed that the growth rate of electrostatic electron cyclotron is increased with the increase of beam speed and also by increasing ambient magnetic field. On the other hand it is reduced due to the increase in number densities ratio of plasma species and by increasing the angle of propagation.